Battery Capacity Estimation Using State of Charge Initialization-On-The-Fly Concept

ABSTRACT

Hybrid-electric and pure electric vehicles include a traction battery comprised of many cells. Controlling a battery system may require that a battery state of charge and a battery capacity be known. The state of charge and battery capacity values may be derived from estimated traction battery model parameters. The accuracy of the estimated model parameters depends on the signal richness and convergence properties of the estimation scheme. Accurate model parameters may be estimated when a persistent excitation condition and an estimation convergence condition are met. If the conditions are not met, active excitation of the battery may be performed to improve the chances of meeting the conditions.

TECHNICAL FIELD

This application is generally related to traction battery state ofcharge and capacity estimation.

BACKGROUND

Hybrid-electric and pure electric vehicles rely on a traction battery toprovide power for propulsion. To ensure optimal operation of thevehicle, various properties of the traction battery may be monitored.One useful property is the battery power capability which indicates howmuch power the battery may supply or absorb at a given time. Anotheruseful property is the battery state of charge which indicates theamount of charge stored in the battery. The battery properties areimportant for controlling operation of the battery duringcharging/discharging, maintaining the battery within safe operatinglimits, and balancing cells of the battery.

Battery properties may be measured directly or indirectly. Batteryvoltages and currents may be measured directly using sensors. Otherbattery properties may require that one or more parameters of thebattery be estimated first. The estimated parameters may includeresistances, capacitances, and voltages associated with the tractionbattery. The battery properties may then be calculated from theestimated battery parameters. Many prior art schemes are available forestimating the battery parameters, including implementing a Kalmanfilter model to recursively estimate the model parameters.

SUMMARY

A battery control system for a vehicle includes a traction batteryhaving a plurality of cells and at least one controller. The controlleris programmed to generate model parameter estimates for the tractionbattery and, in response to a persistent excitation condition and anestimation convergence condition being satisfied, operate the tractionbattery according to a state of charge derived from the model parameterestimates. The persistent excitation condition may be satisfied when

${\alpha_{0}I} \geq {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}\left\lbrack {\begin{matrix}\begin{matrix}\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau} & {i(\tau)}\end{matrix} & {\left. \frac{{i(\tau)}}{\tau} \right\rbrack^{T}*}\end{matrix}{\quad\left\lbrack {{\begin{matrix}\begin{matrix}\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau} & {i(\tau)}\end{matrix} & \left. \frac{{i(\tau)}}{\tau} \right\rbrack^{T}\end{matrix}{\tau}} \geq {\alpha_{1}I}} \right.}} \right.}}$

is satisfied, where T_(pe) is an integration interval, V_(t) is aterminal voltage, V_(oc) is an open circuit voltage, i is a current, andα₀ and α₁ are predetermined values. The estimation convergence conditionmay be satisfied when an error magnitude between at least one of themodel parameter estimates and a corresponding measured model parametervalue is less than a predetermined threshold for a predetermined period.The controller may be further programmed to, in response to at least oneof the persistent excitation condition and the estimation convergencecondition not being satisfied, cause a predetermined number of frequencycomponent amplitudes of battery power demand to exceed a predeterminedmagnitude without affecting acceleration of the vehicle. The controllermay be further programmed to operate the traction battery according to abattery capacity derived from a first state of charge and a second stateof charge, wherein the second state of charge is evaluated afterdetecting at least a predetermined amount of current throughput fromwhen the first state of charge was evaluated. The first state of chargeand the second state of charge may be evaluated within a common ignitioncycle. The first state of charge and the second state of charge may beevaluated when a battery temperature is above a predeterminedtemperature. The controller may be further programmed to schedule thefirst state of charge and the second state of charge to be evaluatedwithin a predetermined time window. The controller may be furtherprogrammed to schedule the predetermined time window such that a timebetween successive predetermined time windows increases as an age of thetraction battery increases. The controller may be further programmed to,in response to at least one of the persistent excitation condition andthe estimation convergence condition not being satisfied within thepredetermined time window, cause a predetermined number of frequencycomponent amplitudes of battery power demand to exceed a predeterminedmagnitude without affecting acceleration of the vehicle.

A vehicle includes a traction battery having a plurality of cells and atleast one controller. The controller is programmed to generate modelparameter estimates for the traction battery and, in response to apersistent excitation condition not being satisfied, cause apredetermined number of frequency component amplitudes of battery powerdemand to exceed a predetermined magnitude without affectingacceleration of the vehicle. The persistent excitation condition may notbe satisfied when

${\alpha_{0}I} \geq {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}\left\lbrack {\begin{matrix}\begin{matrix}\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau} & {i(\tau)}\end{matrix} & {\left. \frac{{i(\tau)}}{\tau} \right\rbrack^{T}*}\end{matrix}{\quad\left\lbrack {{\begin{matrix}\begin{matrix}\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau} & {i(\tau)}\end{matrix} & \left. \frac{{i(\tau)}}{\tau} \right\rbrack^{T}\end{matrix}{\tau}} \geq {\alpha_{1}I}} \right.}} \right.}}$

is not satisfied, where T_(pe) is an integration interval, V_(t) is aterminal voltage, V_(oc) is an open circuit voltage, i is a current, andα₀ and α₁ are predetermined values. The controller may be furtherprogrammed to, in response to an estimation convergence condition notbeing satisfied, cause a predetermined number of frequency componentamplitudes of battery power demand to exceed a predetermined magnitudewithout affecting acceleration of the vehicle. The estimationconvergence condition may not be satisfied when an error magnitudebetween at least one of the model parameter estimates and acorresponding measured model parameter value is greater than apredetermined threshold.

A method of operating a traction battery includes scheduling a timewindow in which to learn a battery capacity. The method furtherincludes, in response to a persistent excitation condition and anestimation convergence condition being satisfied during the window,learning a first state of charge value and, after the batteryexperiences a predetermined amount of current throughput, learning asecond state of charge value. The method further includes operating thetraction battery according to the battery capacity derived from thevalues. The persistent excitation condition may be satisfied when

${\alpha_{0}I} \geq {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}\left\lbrack {\begin{matrix}\begin{matrix}\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau} & {i(\tau)}\end{matrix} & {\left. \frac{{i(\tau)}}{\tau} \right\rbrack^{T}*}\end{matrix}{\quad\left\lbrack {{\begin{matrix}\begin{matrix}\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau} & {i(\tau)}\end{matrix} & \left. \frac{{i(\tau)}}{\tau} \right\rbrack^{T}\end{matrix}{\tau}} \geq {\alpha_{1}I}} \right.}} \right.}}$

is satisfied, where T_(pe) is an integration interval, V_(t) is aterminal voltage, V_(oc) is an open circuit voltage, i is a current, andα₀ and α₁ are predetermined values. The estimation convergence conditionmay be satisfied when an error magnitude between an estimated modelparameter and a corresponding measured model parameter value is lessthan a predetermined threshold for a predetermined period. The methodmay further include causing, in response to at least one of thepersistent excitation condition and the estimation convergence conditionnot being satisfied within the time window, a predetermined number offrequency component amplitudes of battery power demand to exceed apredetermined magnitude without affecting vehicle acceleration. Thefirst and second state of charge values may be learned when a batterytemperature is above a predetermined temperature. The time window may bescheduled such that the time between successive time windows increasesas an age of the traction battery increases.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a hybrid vehicle illustrating typical drivetrainand energy storage components.

FIG. 2 is a diagram of a possible battery pack arrangement comprised ofmultiple cells, and monitored and controlled by a Battery Energy ControlModule.

FIG. 3 is a diagram of an example battery cell equivalent circuit.

FIG. 4 is a graph that illustrates a possible open-circuit voltage (Voc)vs. battery state of charge (SOC) relationship for a typical batterycell.

FIG. 5 is a flowchart of a possible method for calculating batterycapacity incorporating active excitation of the traction battery.

FIG. 6 is a flowchart of a possible method for estimating batteryparameters using active excitation of the traction battery.

FIG. 7 is a diagram depicting possible power flows for describing activeexcitation of the traction battery.

FIG. 8 is a flowchart of a possible method for performing cell balancingusing active excitation of the traction battery.

DETAILED DESCRIPTION

Embodiments of the present disclosure are described herein. It is to beunderstood, however, that the disclosed embodiments are merely examplesand other embodiments can take various and alternative forms. Thefigures are not necessarily to scale; some features could be exaggeratedor minimized to show details of particular components. Therefore,specific structural and functional details disclosed herein are not tobe interpreted as limiting, but merely as a representative basis forteaching one skilled in the art to variously employ the presentinvention. As those of ordinary skill in the art will understand,various features illustrated and described with reference to any one ofthe figures can be combined with features illustrated in one or moreother figures to produce embodiments that are not explicitly illustratedor described. The combinations of features illustrated providerepresentative embodiments for typical applications. Variouscombinations and modifications of the features consistent with theteachings of this disclosure, however, could be desired for particularapplications or implementations.

FIG. 1 depicts a typical plug-in hybrid-electric vehicle (HEV). Atypical plug-in hybrid-electric vehicle 12 may comprise one or moreelectric machines 14 mechanically connected to a hybrid transmission 16.The electric machines 14 may be capable of operating as a motor or agenerator. In addition, the hybrid transmission 16 is mechanicallyconnected to an engine 18. The hybrid transmission 16 is alsomechanically connected to a drive shaft 20 that is mechanicallyconnected to the wheels 22. The electric machines 14 can providepropulsion and deceleration capability when the engine 18 is turned onor off. The electric machines 14 also act as generators and can providefuel economy benefits by recovering energy that would normally be lostas heat in the friction braking system. The electric machines 14 mayalso reduce vehicle emissions by allowing the engine 18 to operate atmore efficient speeds and allowing the hybrid-electric vehicle 12 to beoperated in electric mode with the engine 18 off under certainconditions.

A traction battery or battery pack 24 stores energy that can be used bythe electric machines 14. A vehicle battery pack 24 typically provides ahigh voltage DC output. The traction battery 24 is electricallyconnected to one or more power electronics modules. One or morecontactors 42 may isolate the traction battery 24 from other componentswhen opened and connect the traction battery 24 to other components whenclosed. A power electronics module 26 is also electrically connected tothe electric machines 14 and provides the ability to bi-directionallytransfer energy between the traction battery 24 and the electricmachines 14. For example, a typical traction battery 24 may provide a DCvoltage while the electric machines 14 may require a three-phase ACcurrent to function. The power electronics module 26 may convert the DCvoltage to a three-phase AC current as required by the electric machines14. In a regenerative mode, the power electronics module 26 may convertthe three-phase AC current from the electric machines 14 acting asgenerators to the DC voltage required by the traction battery 24. Thedescription herein is equally applicable to a pure electric vehicle. Fora pure electric vehicle, the hybrid transmission 16 may be a gear boxconnected to an electric machine 14 and the engine 18 may not bepresent.

In addition to providing energy for propulsion, the traction battery 24may provide energy for other vehicle electrical systems. A typicalsystem may include a DC/DC converter module 28 that converts the highvoltage DC output of the traction battery 24 to a low voltage DC supplythat is compatible with other vehicle loads. Other high-voltage loads,such as compressors and electric heaters, may be connected directly tothe high-voltage without the use of a DC/DC converter module 28. Thelow-voltage systems may be electrically connected to an auxiliarybattery 30 (e.g., 12V battery).

The vehicle 12 may be an electric vehicle or a plug-in hybrid vehicle inwhich the traction battery 24 may be recharged by an external powersource 36. The external power source 36 may be a connection to anelectrical outlet. The external power source 36 may be electricallyconnected to electric vehicle supply equipment (EVSE) 38. The EVSE 38may provide circuitry and controls to regulate and manage the transferof energy between the power source 36 and the vehicle 12. The externalpower source 36 may provide DC or AC electric power to the EVSE 38. TheEVSE 38 may have a charge connector 40 for plugging into a charge port34 of the vehicle 12. The charge port 34 may be any type of portconfigured to transfer power from the EVSE 38 to the vehicle 12. Thecharge port 34 may be electrically connected to a charger or on-boardpower conversion module 32. The power conversion module 32 may conditionthe power supplied from the EVSE 38 to provide the proper voltage andcurrent levels to the traction battery 24. The power conversion module32 may interface with the EVSE 38 to coordinate the delivery of power tothe vehicle 12. The EVSE connector 40 may have pins that mate withcorresponding recesses of the charge port 34. Alternatively, variouscomponents described as being electrically connected may transfer powerusing a wireless inductive coupling.

One or more wheel brakes 44 may be provided for decelerating the vehicle12 and preventing motion of the vehicle 12. The wheel brakes 44 may behydraulically actuated, electrically actuated, or some combinationthereof. The wheel brakes 44 may be a part of a brake system 50. Thebrake system 50 may include other components that are required tooperate the wheel brakes 44. For simplicity, the figure depicts a singleconnection between the brake system 50 and one of the wheel brakes 44. Aconnection between the brake system 50 and the other wheel brakes 44 isimplied. The brake system 50 may include a controller to monitor andcoordinate the brake system 50. The brake system 50 may monitor thebrake components and control the wheel brakes 44 to achieve desiredoperation. The brake system 50 may respond to driver commands and mayalso operate autonomously to implement features such as stabilitycontrol. The controller of the brake system 50 may implement a method ofapplying a requested brake force when requested by another controller orsub-function.

One or more electrical loads 46 may be connected to the high-voltagebus. The electrical loads 46 may have an associated controller thatoperates the electrical load 46 when appropriate. Examples of electricalloads 46 may be a heating module or an air-conditioning module.

The various components discussed may have one or more associatedcontrollers to control and monitor the operation of the components. Thecontrollers may communicate via a serial bus (e.g., Controller AreaNetwork (CAN)) or via discrete conductors. In addition, a systemcontroller 48 may be present to coordinate the operation of the variouscomponents.

A traction battery 24 may be constructed from a variety of chemicalformulations. Typical battery pack chemistries may be lead acid,nickel-metal hydride (NIMH) or Lithium-Ion. FIG. 2 shows a typicaltraction battery pack 24 in a simple series configuration of N batterycells 72. Other battery packs 24, however, may be composed of any numberof individual battery cells connected in series or parallel or somecombination thereof. A typical system may have one or more controllers,such as a Battery Energy Control Module (BECM) 76 that monitors andcontrols the performance of the traction battery 24. The BECM 76 maymonitor several battery pack level characteristics such as pack current78, pack voltage 80 and pack temperature 82. The BECM 76 may havenon-volatile memory such that data may be retained when the BECM 76 isin an off condition. Retained data may be available upon the next keycycle.

In addition to the pack level characteristics, there may be battery cell72 level characteristics that are measured and monitored. For example,the terminal voltage, current, and temperature of each cell 72 may bemeasured. A system may use a sensor module 74 to measure the batterycell 72 characteristics. Depending on the capabilities, the sensormodule 74 may measure the characteristics of one or multiple of thebattery cells 72. The battery pack 24 may utilize up to N_(c) sensormodules 74 to measure the characteristics of all the battery cells 72.Each sensor module 74 may transfer the measurements to the BECM 76 forfurther processing and coordination. The sensor module 74 may transfersignals in analog or digital form to the BECM 76. In some embodiments,the sensor module 74 functionality may be incorporated internally to theBECM 76. That is, the sensor module 74 hardware may be integrated aspart of the circuitry in the BECM 76 and the BECM 76 may handle theprocessing of raw signals.

It may be useful to calculate various characteristics of the batterypack. Quantities such a battery power capability and battery state ofcharge may be useful for controlling the operation of the battery packas well as any electrical loads receiving power from the battery pack.Battery power capability is a measure of the maximum amount of power thebattery can provide or the maximum amount of power that the battery canreceive. Knowing the battery power capability allows electrical loads tobe managed such that the power requested is within limits that thebattery can handle.

Battery pack state of charge (SOC) gives an indication of how muchcharge remains in the battery pack. The battery pack SOC may be outputto inform the driver of how much charge remains in the battery pack,similar to a fuel gauge. The battery pack SOC may also be used tocontrol the operation of an electric or hybrid-electric vehicle.Calculation of battery pack SOC can be accomplished by a variety ofmethods. One possible method of calculating battery SOC is to perform anintegration of the battery pack current over time. This is well-known inthe art as ampere-hour integration. One possible disadvantage to thismethod is that the current measurement may be noisy. Possible inaccuracyin the state of charge may occur due to the integration of this noisysignal over time.

A battery cell may be modeled as a circuit. FIG. 3 shows one possiblebattery cell equivalent circuit model (ECM). A battery cell may bemodeled as a voltage source (V_(oc)) 100 having associated resistances(102 and 104) and capacitance 106. V_(oc) 100 represents theopen-circuit voltage of the battery. The model includes an internalresistance, r₁ 102, a charge transfer resistance, r₂ 104, and a doublelayer capacitance, C 106. The voltage V₁ 112 is the voltage drop acrossthe internal resistance 102 due to current 114 flowing through thecircuit. The voltage V₂ 110 is the voltage drop across the parallelcombination of r₂ and C due to current 114 flowing through thecombination. The voltage V_(t) 108 is the voltage across the terminalsof the battery (terminal voltage).

Because of the battery cell impedance, the terminal voltage, V_(t) 108,may not be the same as the open-circuit voltage, V_(oc) 100. Theopen-circuit voltage, V_(oc) 100, may not be readily measurable as onlythe terminal voltage 108 of the battery cell is accessible formeasurement. When no current 114 is flowing for a sufficiently longperiod of time, the terminal voltage 108 may be the same as theopen-circuit voltage 100. A sufficiently long period of time may benecessary to allow the internal dynamics of the battery to reach asteady state. When current 114 is flowing, V_(oc) 100 may not be readilymeasurable and the value may need to be inferred based on the circuitmodel. The impedance parameter values, r₁, r₂, and C may be known orunknown. The value of the parameters may depend on the batterychemistry.

For a typical Lithium-Ion battery cell, there is a relationship betweenSOC and the open-circuit voltage (V_(oc)) such that V_(oc)=f(SOC). FIG.4 shows a typical curve 124 showing the open-circuit voltage V_(oc) as afunction of SOC. The relationship between SOC and V_(oc) may bedetermined from an analysis of battery properties or from testing thebattery cells. The function may be such that SOC may be calculated asf⁻¹(V_(oc)). The function or the inverse function may be implemented asa table lookup or an equivalent equation within a controller. The exactshape of the curve 124 may vary based on the particular formulation ofthe Lithium-Ion battery. The voltage V_(oc) changes as a result ofcharging and discharging of the battery. The term df(soc)/dsocrepresents the slope of the curve 124.

Battery Parameter Estimation

The battery impedance parameters r₁, r₂, and C may change over operatingconditions of the battery. The values may vary as a function of thebattery temperature. For example, the resistance values, r₁ and r₂, maydecrease as temperature increases and the capacitance, C, may increaseas the temperature increases. The values may also depend on the state ofcharge of the battery.

The battery impedance parameter values, r₁, r₂, and C may also changeover the life of the battery. For example, the resistance values mayincrease over the life of the battery. The increase in resistance mayvary as a function of temperature and state of charge over the life ofbattery. Higher battery temperatures may cause a larger increase inbattery resistance over time. For example, the resistance for a batteryoperating at 80 C may increase more than the resistance of a batteryoperating at 50 C over a period of time. At a constant temperature, theresistance of a battery operating at 50% state of charge may increasemore than the resistance of a battery operating at 90% state of charge.These relationships may be battery chemistry dependent.

A vehicle power system using constant values of the battery impedanceparameters may inaccurately calculate other battery characteristics suchas state of charge. In practice, it may be desirable to estimate theimpedance parameter values during vehicle operation so that changes inthe parameters will continually be accounted for. A model may beutilized to estimate the various impedance parameters of the battery.

The model may be the equivalent circuit model of FIG. 3. The governingequations for the equivalent model may be written as:

$\begin{matrix}{{\overset{.}{V}}_{2} = {{{- \frac{1}{r_{2}c}}V_{2}} + {\frac{1}{c}*i}}} & (1) \\{V_{t} = {V_{oc} - V_{2} - {r_{1}*i}}} & (2) \\{{\overset{.}{V}}_{oc} = {{- \frac{V_{oc}}{{SOC}}}\frac{\eta \; I}{Q}}} & (3)\end{matrix}$

where Q is the battery capacity, η is the charge/discharge efficiency, iis the current, {dot over (V)}₂ is the time based derivative of V₂, {dotover (V)}_(oc) is the time based derivative of V_(oc) and dV_(oc)/dSOCis the SOC based derivative of V_(oc).

Combining equations (1) through (3) yields the following:

$\begin{matrix}{\begin{bmatrix}\frac{V_{oc}}{t} \\\frac{V_{2}}{t}\end{bmatrix} = {{\begin{bmatrix}0 & 0 \\0 & {- \frac{1}{C*r_{2}}}\end{bmatrix}*\begin{bmatrix}V_{oc} \\V_{2}\end{bmatrix}} + {\begin{bmatrix}\frac{\frac{V_{oc}}{{SOC}}*\eta}{Q} \\\frac{1}{C}\end{bmatrix}*i}}} & (4) \\{{V_{t}(t)} = {{\left\lbrack {1\mspace{14mu} - 1} \right\rbrack*\begin{bmatrix}V_{oc} \\V_{2}\end{bmatrix}} + {\left\lbrack {- r_{1}} \right\rbrack*i}}} & (5)\end{matrix}$

An observer for equations (4) and (5) can be expressed as follows:

$\begin{matrix}{\begin{bmatrix}\frac{{\hat{V}}_{oc}}{t} \\\frac{{\hat{V}}_{2}}{t}\end{bmatrix} = {{\begin{bmatrix}0 & 0 \\0 & {- \frac{1}{C*r_{2}}}\end{bmatrix}*\begin{bmatrix}{\hat{V}}_{oc} \\{\hat{V}}_{2}\end{bmatrix}} + {\begin{bmatrix}\frac{{- \frac{{\hat{V}}_{oc}}{{SOC}}}*\eta}{Q} \\\frac{1}{C}\end{bmatrix}*i} + {L*\left( {{V_{t}(t)} - {{\hat{V}}_{t}(t)}} \right)}}} & (6) \\{\mspace{79mu} {{{\hat{V}}_{t}(t)} = {{\left\lbrack {1\mspace{14mu} - 1} \right\rbrack*\begin{bmatrix}{\hat{V}}_{oc} \\{\hat{V}}_{2}\end{bmatrix}} + {\left\lbrack {- r_{1}} \right\rbrack*i}}}} & (7)\end{matrix}$

whereV_(t)(t) is the measured cell terminal voltage,{circumflex over (V)}_(t) (t) is an estimate of the cell terminalvoltage,{circumflex over (V)}_(oc) is an estimate of the cell open-circuitvoltage,{circumflex over (V)}₂ is an estimate of the voltage across thecapacitive element, andL is a gain matrix chosen so that the error dynamics are stable underall conditions.

The above model provides an estimate of the open-circuit voltage and thevoltage across the capacitive network of the ECM. As the observer errorapproaches zero, the estimates may be considered to be sufficientlyaccurate. The above model relies on impedance parameter values such asr₁, r₂, and C. In order for the model to be accurate, the parametervalues may need to be known with sufficient accuracy. As the parametervalues may vary over time, it may be desirable to estimate the parametervalues.

A possible representation of the battery parameter learning model fromabove may be as follows:

$\begin{matrix}{\left\lbrack {{V_{oc}(t)} - {V_{t}(t)}} \right\rbrack = {\left\lbrack {\frac{{V_{t}(t)}}{t} - {\frac{{V_{oc}(t)}}{t}\mspace{14mu} {i(t)}\mspace{20mu} \frac{{i(t)}}{t}}} \right\rbrack*\begin{bmatrix}{r_{2}*C} \\{r_{1} + r_{2}} \\{r_{1}*r_{2}*C}\end{bmatrix}}} & (8)\end{matrix}$

A Kalman filter-based recursive parameter estimation scheme can be usedto estimate the impedance parameters (r₁, r₂, C) of the observer ofequations (6) and (7). A discretized form of these parameters can beexpressed as a function of the system states as follows:

$\begin{matrix}{\left\lbrack \left( {{V_{oc}(k)} - {V(k)}} \right) \right\rbrack = {\left\lbrack {\frac{T_{s}}{2}\left( {\left( {{V_{t}(k)} - {V_{oc}(k)}} \right) - \left( {{V_{t}\left( {k - 1} \right)} - {V_{oc}\left( {k - 1} \right)}} \right)} \right)\mspace{14mu} {i(k)}\mspace{14mu} \frac{T_{s}}{2}*\left( {{i(k)} + {i\left( {k - 1} \right)}} \right)} \right\rbrack*\begin{bmatrix}{r_{2}*C} \\{r_{1} + r_{2}} \\{r_{1}*r_{2}*C}\end{bmatrix}}} & (9)\end{matrix}$

The Kalman filter recursive parameter estimation can be achieved byexpressing equation (8) in the form:

Y(k)=Φ^(T)(k)*Θ(k)  (10)

where Φ is referred to as the regressor and Θ is the parameter vector.

The Kalman filter estimation scheme may then expressed by the followingequations:

$\begin{matrix}{{\hat{\Theta}\left( {k + 1} \right)} = {{\hat{\Theta}(k)} + {{K(k)}*\left( {{Y\left( {k + 1} \right)} - {{\Phi^{T}(k)}*{\hat{\Theta}(k)}}} \right)}}} & (11) \\{{K\left( {k + 1} \right)} = {{Q\left( {k + 1} \right)}*{\Phi \left( {k + 1} \right)}}} & (12) \\{{Q\left( {k + 1} \right)} = \frac{P(k)}{R_{2} + \left( {{\Phi^{T}\left( {k + 1} \right)}*{P(k)}*{\Phi \left( {k + 1} \right)}} \right)}} & (13) \\{{P\left( {k + 1} \right)} = {{P(k)} + R_{1} - \frac{{P(k)}*{\Phi (k)}*{\Phi^{T}(k)}*{P(k)}}{R_{2} + \left( {{\Phi^{T}\left( {k + 1} \right)}*{P(k)}*{\Phi \left( {K + 1} \right)}} \right)}}} & (14)\end{matrix}$

where {circumflex over (Θ)}(k+1) is the estimate of the parameters fromequation (8), K, Q, and P are calculated as shown, and R₁ and R₂ areconstants. After the parameters are calculated using the Kalman filteralgorithm, the parameters can be used in equations (6) and (7) to obtainan estimate of the state variables. Once V_(oc) is estimated, the valueof SOC can be determined according to FIG. 4. Other parameter estimationschemes, such as least-squares estimation, may also be utilized.

The above parameter estimation requires a value of V_(oc). V_(oc) may becalculated from equation (3). At the start of an ignition cycle afterthe battery is rested, the terminal voltage and the open-circuit voltagemay be considered to be equal. A measurement of the terminal voltage maybe used as the starting value for V_(oc). Equation (3) may then be usedto estimate the open-circuit voltage as a function of current. Oncereasonably accurate parameter estimates are available, the open-circuitvoltage estimate derived from equations (6) and (7) may be used.

One possible model may consider the current (i) as the input, thevoltage (V₂) as a state, and the term (V_(oc)−V_(t)) as an output. Thebattery impedance parameters (r₁, r₂ and c) or their variouscombinations may also be treated as states to be identified. Once thebattery ECM parameters and other unknowns are identified, the SOC andthe power capability may be calculated based on operating limits of abattery voltage and current, and the current battery state.

Various values may be measured on a per-cell basis or on an overall packbasis. For example, the terminal voltage, V_(t), may be measured foreach cell of the traction battery. The current, i, may be measured forthe entire traction battery since the same current may flow through eachcell. Different pack configurations may require different combinationsof measurements. The estimation model may be performed for each cell andthe cell values may then be combined to arrive at an overall pack value.

Another possible implementation may utilize an Extended Kalman Filter(EKF). An EKF is a dynamic system, that is governed by equations of thefollowing form:

x _(k) =f(x _(k-1) ,u _(k-1) ,w _(k-1))  (15)

z _(k) =h(x _(k) ,v _(k-1))  (16)

where: x_(k) may include the state V₂ and the other battery ECMparameters; u_(k) is the input (e.g., battery current); w_(k) is theprocess noise; z_(k) may be the output (e.g., V_(oc)−V_(t)); and v_(k)is the measurement noise.

One possible set of states for the governing equations for theequivalent model may be chosen as follows:

$\begin{matrix}{x = {\begin{bmatrix}x_{1} \\x_{2} \\x_{3} \\x_{4}\end{bmatrix} = \begin{bmatrix}V_{2} \\{1\text{/}\left( {r_{2}C} \right)} \\{1\text{/}C} \\r_{1}\end{bmatrix}}} & (17)\end{matrix}$

The corresponding state space equations of equations (1) and (2), indiscrete or continuous time, may be expressed in the form of Equations(3) and (4). Based on the system model described, an observer may bedesigned to estimate the extended states (x₁, x₂, x₃ and x₄). Once thestates are estimated, the voltage and impedance parameter values (V₂,r₁, r₂, and C) may be calculated as a function of the states as follows:

{circumflex over (V)} ₂ =x ₁  (18)

{circumflex over (r)} ₁ =x ₄  (19)

{circumflex over (r)} ₂ =x ₃ /x ₂  (20)

Ĉ=1/x ₃  (21)

The complete set of EKF equations consists of time update equations andmeasurement update equations. The EKF time update equations project thestate and covariance estimate from the previous time step to the currenttime step:

{circumflex over (x)} _(k) ⁻ =f({circumflex over (x)} _(k-1) ,u_(k-1),0)  (22)

P _(k) ⁻ =A _(k) P _(k-1) A _(k) ^(T) +W _(k) Q _(k-1) W _(k) ^(T)  (23)

where: {circumflex over (x)}_(k) ⁻ represents a priori estimate ofx_(k); P_(k) ⁻ represents a priori estimate error covariance matrix;A_(k) represents the Jacobian matrix of the partial derivatives of f(x,u, w) with respect to x; P_(k-1) represents a posteriori estimate errormatrix of last step; A_(k) ^(T) represents transpose of matrix A_(k);W_(k) represents the Jacobian matrix of the partial derivatives of f(x,u, w) with respect to process noise variable w; Q_(k-1) represents aprocess noise covariance matrix, and W_(k) ^(T) represents transpose ofmatrix W_(k).

The matrix A_(k) may be constructed from the set of state equationsdefined by combining the system equations and the system states. Theinput, u, in this case, may include the current measurement, i.

The measurement update equations correct the state and covarianceestimate with the measurement:

K _(k) =P _(k) ⁻ H _(k) ^(T)(H _(k) P _(k) ⁻ H _(k) ^(T) +V _(k) R _(k)V _(k) ^(T))⁻¹  (24)

{circumflex over (x)} _(k) ={circumflex over (x)} _(k) ⁻ +K _(k)(z _(k)−h({circumflex over (x)} _(k) ⁻,0))  (25)

P _(k)=(I−K _(k) H _(k))P _(k) ⁻  (26)

where: K_(k) represents the EKF gain; H_(k) represents the Jacobianmatrix of the partial derivatives of h with respect to x; H_(k) ^(T) isthe transpose of H_(k); R_(k) represents a measurement noise covariancematrix; V_(k) represents the Jacobian matrix of the partial derivativesof h with respect to measurement noise variable v; z_(k) represents themeasured output values; and V_(k) ^(T) is the transpose of V_(k).

In the EKF model, the resistance and capacitance parameters may beassumed to be slowly varying and have a derivative of zero. Theestimation objective may be to identify the time-varying values of thecircuit parameters. In the above model, three impedance parameters maybe identified: r₁, r₂, and C. More comprehensive models may additionallyestimate V_(oc) as a time-varying parameter. Other model formulationsmay incorporate a second RC pair to represent a slow and a fast voltagerecovery dynamics. These formulations may increase the number of statesin the model. Other battery properties may then be calculated based onthe identified parameters or may be estimated as part of the model.

One of ordinary skill in the art can construct and implement the EKFgiven a set of model equations. The system of equations described aboveis one example of a system model for a battery system. Otherformulations are possible and the methods described will work equallywell on other formulations.

In the above example, i and V_(t) may be measured quantities. Thequantity V_(oc) may be derived from the measured quantities and theparameter estimates from the EKF. Once V_(oc) is known, the state ofcharge may be calculated based on FIG. 4. Knowing the above parametersmay allow one to calculate other battery properties.

Battery Capacity Estimation

There are two main categories of battery capacity estimation algorithms.The first category bases the calculation on the definition ofcapacity—battery throughput divided by a difference in state of charge(SOC) values. This approach is based on knowledge of two separate SOCvalues obtained independent of battery capacity. The calculation may beexpressed as:

$\begin{matrix}{Q = {\frac{\int_{Ti}^{Tf}{i{t}}}{{SOC}_{i} - {SOC}_{f}} = \frac{Throughput}{{SOC}_{i} - {SOC}_{f}}}} & (27)\end{matrix}$

where SOC_(i) and SOC_(f) are the state of charge values at times T_(i)and T_(f) respectively. The battery throughput may be defined as theintegral of current over a time period. When implemented in acontroller, the integral may be replaced by a summation of currentvalues multiplied by the sample time.

Systems using the above formulation are present in the prior art. Oneprior art approach is to obtain the state of charge values over twokey-on/key-off cycles. For a lithium-ion battery, it is well-known thatafter the battery has been resting a sufficient time, the terminalvoltage will be very close to the open-circuit voltage of the battery(i.e., V_(t)=V_(oc)). The terminal voltage may be measured at power-upand the state of charge may be derived from the open-circuit voltage(e.g., FIG. 4). The throughput may be calculated over each ignitioncycle and stored in a non-volatile memory for use in the next ignitioncycle.

The accuracy of the capacity definition approach depends on severalfactors. The calculation is dependent upon two key-on and key-off cyclesto obtain the SOC difference. The two ignition cycles must be separatedby enough time so that the battery is sufficiently rested and enoughcurrent throughput through the battery. The result further depends onthe key-on voltage readings for the open-circuit voltage values. Tocalculate throughput, current integration may be used which includescurrent sensor inaccuracy and current integration error. Current leakageduring key-off periods may not be accounted for. In addition, thetemperature change between the two key cycles may be large. The resultof these inaccuracies is that the battery capacity may be difficult tocalculate accurately using such an approach. In particular, smallchanges in the battery capacity may not be discernible due to theinaccuracies described.

The impact of voltage sensor inaccuracy on battery capacity using theabove two key-on/key-off cycles may be expressed as follows:

$\begin{matrix}{{\Delta \; Q} = \frac{\left( {\int_{0}^{T}{{i(\tau)}{\tau}}} \right)*\left( {\Delta \; V} \right)*\left( {\frac{f}{V}{{{OCV}_{1} + \frac{f}{V}}}{OCV}_{2}} \right)}{\left( {{f\left( {OCV}_{2} \right)} - {f\left( {OCV}_{1} \right)}} \right)^{2}}} & (28)\end{matrix}$

where ΔQ is the potential capacity estimation error, OCV₁ and OCV₂ arethe two key-on/key-off voltage readings in which f(OCV_(x)) defines theSOC at that particular voltage, T is the total time used in currentintegration, and ΔV represents the voltage sensor inaccuracy. df/dV isthe derivative of the SOC-OCV curve at the given OCV value.

As a worst case example, consider a 25 Ah cell with an SOC change of 20%(5 Ah throughput) as measured at the start of two separate ignitioncycles. Assuming a voltage sensor inaccuracy of 10 mV and a df/dV ofapproximately 1, the capacity estimation error due to voltage sensorinaccuracy will be ΔQ=9000 A-s. or approximately 10% of the batterycapacity.

The second category of battery capacity estimation algorithms learns thebattery capacity based on system identification theory in which thebattery capacity is learned as part of a battery model. The model-basedapproach also has some limitations. Normally, the battery capacity isonly a weakly identifiable variable. In particular, when many otherbattery parameters are lumped together, the weak identifiability of thebattery capacity makes a model-based Kalman filter approach impracticalwhen the battery measurements are corrupted by noise, sensorinaccuracies, or battery modeling errors. Based on this, it may bedesirable to eliminate the errors induced in the battery capacityestimation by the open-circuit voltage sensing error, unaccountedleakage current, and temperature changes between two consecutive drivecycles.

A battery model may be periodically executed in a vehicle controllerthroughout the battery life. Based on the learned model parameters, anSOC observer may be designed such that SOC may be accurately estimated.The SOC observer may be implemented and parameter estimates may beobtained.

There are several approaches that may be applied to determine when toestimate the battery parameters. One approach may be to learn theparameters at all times. However, there are drawbacks to this approach.The equivalent circuit model is only an approximation of the realbattery behavior. Sensor biases and inaccuracies may be present in themeasurement signals. These factors contribute to inaccuracies in theparameter estimation, particularly when the input is not sufficientlyrich or persistently excited. An input is not sufficiently rich if theinput does not provide proper excitation to the battery to allowaccurate parameter estimation. The richness or persistency of theexcitation may also depend on the presence of various frequencies in theinput signal. The input signal for a traction battery may be a batterypower demand. For example, operating at a constant current may notprovide enough variation to ascertain dynamic properties of the model.

Another approach may be to bypass the parameter estimation when theinput is not considered sufficiently rich. An open-loop observer may beused to estimate battery state variables during these intervals. Thisapproach involves detecting when the conditions are not sufficientlyrich and may provide better estimates than the continual learningapproach. However, an issue with this approach may be the effect of anextended period where the input is not sufficiently rich for parameterestimation. The open-loop observer may provide sufficient estimatesinitially, but over time the estimates may become inaccurate.

Issues may arise when the battery system operates for an extended periodof time under conditions that are not sufficiently rich to accuratelylearn the parameters. In these situations, the parameters may not beaccurately learned for a long period time. The last learned values maydiffer significantly from the true value at the present time. Forexample, the resistance r₁ in the circuit model may increase as thebattery ages. This may cause an unacceptable increase in the batterypower capability error.

Another approach may be to actively excite the battery for parameterestimation purposes. The system may try to generate a battery input viatorque modulation or other control actions to create an input that ispersistently excited for parameter estimation purposes. The batterypower demand may be such that sufficient frequency components areexcited such that accurate parameter estimation may be achieved. Thecontrols actions are ideally transparent to the end users. For example,any modification to the traction battery power demand should not affectacceleration of the vehicle.

Persistent Excitation and Estimation Convergence Conditions

In order to effectively learn the battery parameter values, inputconditions to the estimation model may need to be valid. When validinput conditions are satisfied, the battery parameter values may belearned with sufficient accuracy. In the absence of valid inputconditions, battery parameter learning may result in inaccurate values.

One condition that may be met is a persistent excitation condition. Inorder to effectively estimate the parameters shown above, an associated“persistent excitation” matrix (PEM) may be defined as follows:

$\begin{matrix}{{PEM} = {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{14mu} {i(\tau)}\mspace{14mu} \frac{{i(\tau)}}{\tau}} \right\rbrack^{T}*{\quad{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{14mu} {i(\tau)}\mspace{14mu} \frac{{i(\tau)}}{\tau}} \right\rbrack {\tau}}}}}}} & (29)\end{matrix}$

where T_(pe) is the time interval over which the integration takesplace. Alternatively, instantaneous values may be utilized (e.g.,eliminate the integration in the above equation). The integration mayhelp filter out noisy signals and prevent rapid changes of the signals.The discrete form of equation (9) may also be used to formulate the PEM.For example, T_(pe) may be set to 5 seconds so that the PEM elements areintegrated over a 5 second interval. For the parameter estimates to beaccurate, the PEM may need to meet certain positive semi-definitenessproperties. A matrix, P, is positive semi-definite if x^(T)Px≧0 for allx. The persistent excitation condition is that matrices calculated as(PEM−α₁I) and (α₀I−PEM), where I is an identity matrix, are positivesemi-definite. The persistent excitation condition may be expressed asα₀I≧PEM≧α₁I, but care must be taken as the expression is a matrixexpression and not a scalar expression. If a matrix is positivesemi-definite, all eigenvalues of the matrix are non-negative. A matrix,P, that is positive definite (x^(T)Px>0 for all x) is invertible. Theexpression α₀I≧PEM≧α₁I may be referred to as a persistent excitationcondition. Note that the above PEM is of a form associated with thechosen estimation model. Different model formulations may result in adifferent PEM and may have a different persistent excitation condition.

In other words, if the regressor-based persistent excitation matrixsatisfies certain positive definiteness conditions, then the parameterestimates may be unbiased. When the persistent excitation condition ismet, the parameters may be accurately learned as the input signals maybe considered to be sufficiently rich. The values α₀ and α₁ may definean upper and lower bound for the positive semi-definiteness of thepersistent excitation matrix. The values α₀ and α₁ may depend oncharacteristics of the battery system. When the positive-definitenesscriteria for the regressor-based matrix are satisfied, the inputconditions may be considered to be valid. The values of T_(pe), α₀ andα₁ may be adjusted to modify the persistent excitation condition to meetsignal richness requirements for different purposes.

The persistent excitation condition may indicate that input conditionsare valid for parameter estimation but does not necessarily indicatethat the parameter estimation has converged to the true values.Additional monitoring of estimation errors may be performed to ascertainwhen the parameter estimates are converging to the actual values. Anestimation convergence condition may be monitored to ascertain theconvergence of the parameter estimates. One way to ascertain the qualityof the parameter estimates may be to monitor the estimation error of oneor more modeled variables or parameters. An error between an estimatedvalue and a measured value may be monitored. When the magnitude of theerror is bounded by a certain value over a predetermined time period,the parameter estimates may be considered to be acceptable. For example,the projection error (V_(t)(t)−{circumflex over (V)}_(t)(t)) fromequation (6) may be monitored for convergence. The estimationconvergence condition may be that the magnitude of the estimation errorbe less than a predetermined threshold for a predetermined time period.One or more parameter errors may be monitored and the selection of themonitored values may depend on the model and measurements that areavailable.

When the battery is sufficiently excited (e.g., persistent excitationcondition satisfied) and the estimation error in the parameter observerremains bounded for a given period of time (e.g., estimation convergenceconditions satisfied), the SOC error may also be bounded by apredetermined value. The SOC error bound may be designed to besufficiently small and the SOC value learned by the SOC observer may beused to initialize the ampere-hour integration based SOC method.Calibration of SOC error bound may be application specific. For example,for vehicle drive control, a 2% accuracy may be sufficient. However, forbattery capacity estimation, a more accurate bound may be desired. Adifferent error magnitude threshold may be used for the estimation errordepending on the desired accuracy. A lower threshold may improveaccuracy of the estimation.

The above persistent excitation condition may be implemented in acontroller. The controller may be programmed to calculate each elementof the matrix and ascertain the positive semi-definiteness condition. Ifthe persistent excitation conditions of positive semi-definiteness aremet, a flag may be set indicating that the input is sufficiently rich orpersistently excited for accurate parameter estimation. This flag may beused to initiate a parameter estimation cycle. Alternatively, parametersmay be estimated at all times but the estimated values may be ignoreduntil the persistent excitation condition is satisfied for apredetermined period of time.

Once the battery is sufficiently excited and the estimation error isbounded for a given period of time, the SOC error may be consideredsufficiently small. This may be referred to as SOCinitialization-on-the-fly (SIOF). This term is used as an accurateestimate of the open-circuit voltage may be obtained, and hence anaccurate value for SOC, at any time while the controller is operating,not just at startup. The SOC values may be obtained “on-the-fly” or atany time as opposed to the prior art “startup-only” SOC initialization.Two such events during a common ignition cycle may be used to replacethe two key-on voltage readings used in the prior art. This approachdoes not depend on key-on and key-off cycles to determine SOC values.The SOC values may be obtained at any time while the system isoperating. This scheme allows the battery capacity to be calculatedwhenever the SOC error is sufficiently small. The SIOF condition may bemet when the battery is sufficiently excited and the estimation error inthe model parameter observer remains bounded for a given period of time.

SOC estimation error due to voltage and current sensor accuracy maystill remain. The most significant error may be:

K(k)*(∥ΔV∥+( r ₁ *∥ΔI∥))  (30)

where K(k) is a gain, normally non-stationary, ΔV and ΔI are voltage andsensor inaccuracies, respectively, and r₁ is the battery internalresistance value at a given temperature and SOC. The impact of voltageand current sensor inaccuracies may be reduced by limiting capacitylearning for temperatures above a certain value and setting the observergain to a smaller value. The error estimation is not impacted by changesin the capacity.

Given the above formulation, a system may determine if the batterysystem is persistently excited such that acceptable estimation resultsmay be achieved. One technique may be to monitor the persistentexcitation condition described above. A passive approach might monitorthe persistent excitation condition and perform parameter learning whenthe condition is satisfied. The passive approach relies on normaloperation of the battery and learns the parameter values when theconditions are proper.

An active excitation approach may create conditions such that thepersistent excitation condition is satisfied. This may include operatingthe battery pack in such a manner as to satisfy the persistentexcitation conditions. This may require the controller to command otherdevices or subsystems to operate by providing power to or receivingpower from the battery. Ideally, this operation should be transparent tothe vehicle occupants. The active excitation approach may allow theparameters to be learned at any time with the addition of the activeexcitation of the battery system.

Scheduling Battery Capacity Based on Learning Window

Once a method of calculating battery capacity is defined, a relatedissue is scheduling the battery capacity learning. A system may need todetermine how often battery capacity needs to be learned. There may betradeoffs between the amount of execution time spent on capacitylearning and the accuracy of the battery capacity value. Studiesindicate that a lithium-ion battery capacity fade follows asquare-root-of-time law under normal temperatures. The magnitude ofcapacity fade is larger earlier in the battery life. Based on thisobservation, battery capacity learning may be scheduled based oncalendar life of the battery. Since the magnitude of change is greaterearlier in battery life, learning events may be scheduled morefrequently early in the battery life. That is, as the age of the batteryincreases, the time interval between successive battery capacitydeterminations may be increased.

The persistent excitation and estimation convergence conditionsdescribed above may provide a check as to when battery capacity may beaccurately estimated. There may be situations where conditions are notmet for long periods of time. Under these situations, “activeexcitation” of the battery for estimation purposes may be initiated.Active excitation of the battery attempts to cause battery operatingconditions such that the persistent excitation condition for capacityestimation is satisfied. When the persistent excitation condition issatisfied, the estimation convergence condition may also be satisfied.

Capacity learning may be scheduled according to an acceptable capacityerror and the square-root-of-time law of capacity fade. Scheduling maybe evenly distributed based on in-use time. One example of a system thatcalculates battery power capacity is shown in FIG. 5. A predeterminedschedule of learning windows may be defined and stored in controllermemory. There may be many methods of setting the learning windows. Forexample, the expected capacity fade may be analyzed and learning windowsmay be created that correspond to equal changes in capacity.

For each scheduled capacity learning event, two time values may bedefined. A learn date (LD) may be defined and may be a date and time inrelative calendar terms associated with beginning of life calendar timeand defines a desired time that the capacity should be learned. A latestlearning date (LLD) may be defined that may be a date and time inrelative calendar terms associated with the beginning of life calendartime and defines the latest time at which the capacity should belearned. The two values may define a target window of time in which thecapacity may be learned. A sequence of capacity learning events, eachevent having associated time values defined, may be predetermined andstored in controller memory.

The controller may be programmed to maintain a battery life time counter(t) that indicates the elapsed time since the battery has been deployed.The battery life time counter (t) may be reset to zero at the start ofthe battery life time. The life time counter may be based on a calendardate and time that is maintained by a controller within the vehicle. Thebattery life time counter (t) may be incremented periodically over thelife time of the battery to reflect the time since the start of batterylife. The sequence of learning dates may be relative to the batterybeginning of life. At vehicle key-on, the battery life time counter maybe compared to the learning schedule to determine if battery capacityneeds to be calculated.

At vehicle key-on 200, the controller may read the capacity learningschedule into memory 202. The capacity learning schedule may becomprised of a sequence of pairs of learn dates (LD) and latest learningdates (LLD). The pairs may be indexed such that an index, j, into thelearning schedule returns the j^(th) learn date and the j^(th) latestlearn date. Each pair in the learning schedule may have an associatedflag that indicates whether the learning has been completed yet for thatpair. The current learning schedule index may be ascertained 204 fromthe battery life time counter and the learn dates of the learningschedule. The learning schedule may be searched to find the next indexfor which the learning has not yet been completed. The index, j, of thispair may be retained during controller operation for accessing thelearning schedule.

Before calculating battery capacity, the battery temperature, T_(batt),may be checked 206. To improve the estimation, capacity may be learnedwhen the battery temperature is above a predetermined threshold,T_(cal). If the temperature is below the predetermined threshold,parameter estimation may be delayed until the temperature is above thethreshold.

As described earlier, the learning schedule may define a window of timein which to calculate the battery capacity. The window may be defined bythe index and the two time values at that index—a learn date [LD(j)] anda latest learning date [LLD(j)]. The controller may compare the batterylife time counter to the indexed learn date 208. If the battery lifetime counter, t, has not reached the indexed learn date, the system maycontinue to check the temperature 206 and the time 208. In this case,the battery capacity may not be estimated at the present time.

If the battery life time counter exceeds the indexed learn date, then apassive excitation (PE) condition may be checked 210. The PE conditionis met when the persistent excitation condition and the estimationconvergence condition are satisfied. If the PE condition is met, thecontroller may store the present open-circuit voltage, or alternativelythe state of charge associated with the open-circuit voltage, and resetelapsed time (te) and throughput counter (TP) values 216.

If the PE condition is not met, the battery life time counter may becompared to the currently indexed latest learning date [LLD(j)] 212. Ifthe battery life time counter exceeds the currently indexed LLD, thenactive excitation of the traction battery may be initiated 214. If thebattery life time counter does not exceed the currently indexed LLD,then the execution may go back to checking the PE condition 210. In thatcase in which active excitation is applied, after the active excitationis applied, the estimated open-circuit voltage may be sampled 216. Thismay assume that the active excitation process is executed for a durationthat guarantees that the PE condition is met. Alternatively, afteractive excitation is applied, the PE condition may be monitored toensure that the active excitation created the proper battery powerdemand.

A first open-circuit voltage value, V_(oc) ¹, may be stored as thepresent learned value for the open-circuit voltage. This value may bethe result of the battery impedance parameter estimation model that isoperating. A throughput (TP) value may be reset to a value of zero. Anelapsed time, t_(e), value may be reset to zero. The throughput valuemay be used to accumulate the current using an ampere-hour integration.During operation, the throughput value may be incremented by the productof the current and the sampling period.

Once the first open-circuit voltage is stored, the battery temperaturemay be compared to a calibrated temperature 218. If the batterytemperature, T_(batt), does not exceed the calibrated temperature,T_(cal), the learning may be reset and the execution may return tochecking the PE condition 210. When the battery temperature exceeds thethreshold, other criteria may be checked 220.

The throughput (TP) may be compared a threshold (TP_(cal)). In addition,the elapsed time, t_(e), may be compared to a calibrated time, t_(cal).If the throughput exceeds the throughput threshold and the elapsed timeis less than a calibrated value, then the system may check the PEcondition 222 again. The time and throughput conditions may ensure thatthe battery has been operated enough so that a reasonable SOC differenceis present. Should the criteria not be met, the values of throughput(TP) and the elapsed time (t_(e)) may be incremented 226.

The throughput (TP) may be incremented by a product of the sampling timeand the measured current. The elapsed time may be incremented by thesampling time at each execution interval. Execution may then be returnedto the temperature check 218.

When the TP and t_(e) criteria 220 are met, the PE condition may bechecked 222. If the PE condition is met, the system may store a secondopen-circuit voltage value, V_(oc) ², 230 for the final calculation ofbattery capacity. If the PE condition is not met, the controller maycheck to see if the currently indexed latest learning date is exceeded224. The battery life time counter may be compared to the currentlyindexed latest learning date. If the battery life time counter exceedsthe currently indexed LLD, then active excitation may be initiated 228.Should the battery life time counter not exceed the currently indexedLLD then the execution may increment the TP and t_(e) values 226.

After active excitation, the second open-circuit voltage may be stored230 as the current open-circuit voltage value from the model. The activeexcitation may need to be applied for some period of time to allow thePE condition to be satisfied. Once again, an alternative may be toactually check the PE condition to ensure that the active excitationworked properly.

Once the second open-circuit value is saved, the capacity may becalculated 232 as follows:

$\begin{matrix}{Q_{new} = \frac{Throughput}{{SOC}_{1} - {SOC}_{2}}} & (31)\end{matrix}$

The capacity may optionally be filtered 232 using a low-pass filter.Once the capacity value is learned, the capacity learning for thescheduled event may be considered complete. A flag may be stored withthe learning schedule entry to indicate that the capacity learning forthis entry has been completed. Note that the SOC values may be derivedas a function of the open-circuit voltage as discussed in relation toFIG. 4. The capacity value may be filtered by defining a value, a, thatweighs the contribution of the currently calculated capacity and theprevious capacity value. This may be expressed as:

Q _(new) =αQ _(new)+(1−α)Q _(old)  (32)

where Q_(old) represents the previous capacity value.

Once the new battery capacity is calculated, the learning is completedfor the indexed learn date 234. The battery capacity for the index maybe stored. A flag may also be stored with the index to indicate thatlearning for the indexed schedule values is completed. The execution maythen stop 236 until subsequent key-on cycles at which time the processmay be repeated as a new learning schedule index may be available.

In some situations, the inputs necessary to provide a persistentexcitation may not be present to meet the criteria for passiveexcitation. This may be due to vehicle controls and operator drivinghabits. In such a situation, the battery life time counter may exceedthe latest learning date for the scheduled learning event. Should thebattery life time counter exceed the latest learning date without thecapacity learning being completed, the system may request that activeexcitation be performed.

Active excitation may attempt to use other vehicle controls (forexample, high-voltage components such as electric air conditioning,electric heater, power steering, or electric vehicle motor control) suchthat the battery inputs satisfy the persistent excitation criteria.Ideally, the operation of the additional components will be performed ina manner transparent to the operator. The active excitation may beconstructed such that a net power at the wheels does not change duringthe operation.

To summarize, the battery capacity calculation does not necessarilyrequire two open circuit voltage readings for SOC obtained at the startof two separate ignition cycles. A model-based system may be used toestimate battery capacity when SOC estimates have the highestconfidence. Using the above method, it may be desirable that the currentintegration and SOC values be independent of one another to avoidcircular calculations. A pure ampere-hour integration based SOCcalculation makes the capacity estimate circular as both the numeratorand denominator of the equation would rely on the current integration.The system described uses an ampere-hour integration for the numeratorbut relies on model-based parameters for the denominator, thus avoidingthe circular calculations. In addition, if conditions are such that SOCestimates have a low confidence, the controller may operate the tractionbattery to achieve conditions in which high confidence estimates may beobtained.

It is easily shown that the effect of errors in the capacity value havenegligible effect on the SOC estimation from the model. The derivativeof the open-circuit voltage may be expressed as:

$\begin{matrix}{{\overset{.}{V}}_{oc} = {{- \frac{{f({soc})}}{{soc}}}*\frac{1}{Q}*I}} & (33)\end{matrix}$

where Q is the charge capacity and I is the battery current. In a systemin which the above equation is used in a model to calculate V_(oc), theerror in the open-circuit voltage during a constant current dischargemay be approximated as:

$\begin{matrix}{{V_{oc} - V_{{oc}\; \_ \; {est}}} = {{- \frac{f}{{SOC}}}*I*\frac{\Delta \; Q}{Q^{2}}*\frac{1}{L}}} & (34)\end{matrix}$

where ΔQ represents an error in the capacity and L represents theobserver gain. The value of ΔQ may be considered to be small comparedwith Q. As an example, assume that I=100 Amps, L=100, df/dSOC=1, Q=25Amp-hr=90000 Amp-sec, and ΔQ=1000 Amp-sec. Using these values, the errorbecomes 1/8,100,000 Volts which is nearly zero. Based on the erroranalysis, it is reasonable to rely on a SOC estimation using an observerbased on a battery model even when the battery capacity used in themodel is not perfectly accurate.

Advantages of the capacity learning scheme is that the impact of voltagesensor errors and unaccounted leakage current on capacity estimation isreduced. Passive learning using battery input based on driver input andvehicle controls design may be used. Active excitation that istransparent to the driver may also be used when necessary.

The above method provides an accurate estimation of SOC based on themodel parameter estimates. Once SOC is ascertained, the traction batterymay be operated according to the SOC values. The traction battery may befurther operated based on the battery capacity estimate.

Scheduling Active Excitation for Cell Balancing

Within a battery comprised of many connected cells, the state of chargeof the cells may become unbalanced for many reasons includingmanufacturing variations, cell fading at different rates due totemperature distribution within the battery pack, and internal leakageat different rates due to chip design. Battery cell imbalance may bedefined as a difference between SOC of the cells. Many productionbattery packs include a cell balancing function in which cell balancingcontrol is triggered when a magnitude of an SOC difference between cellsexceeds a predetermined value.

Cell balancing is a process that attempts to equalize the SOC of thecells by adding or subtracting charge from the affected cells. Prior artsystems may initiate cell balancing when a magnitude of an SOCdifference between the cells is greater than a threshold. When the SOCdifference magnitude between the cells is less than a second threshold,cell balancing may be terminated. Due to inaccuracies in the SOC values,prior art system may tend to over balance the cells leading to wastedenergy.

Various methods of performing cell balancing are possible. Some systemsmay include a switch across each cell that can selectively switch acircuit element across the cell. The circuit element may allow the cellto discharge. Alternatively, a switch may selectively connect cellstogether such that one cell discharges while charging another cell. Cellbalancing may be achieved by selectively charging and discharging thecells of the battery until all cells have approximately the same stateof charge. The scheme to be described may be applicable to any cellbalancing hardware configuration.

Methods of calculating SOC, such as ampere-hour integration andmodel-based observers may be biased from the true values. For a systemthat relies on a cell voltage measurement at key on, the cell voltagesensor accuracy may cause inaccurate SOC values. Due to tolerances inthe cell voltage measurements, SOC values may be inaccurate atinitialization. Cell imbalances may be falsely observed due to thevoltage measurement inaccuracy. Since the cell balancing strategy relieson SOC, it is desirable to ensure that the SOC values are accurateenough to initiate and terminate cell balancing.

Cell balancing may be initiated when a magnitude of an SOC differencebetween cells is above a predetermined value. After performing cellbalancing for a period of time, the SOC difference may be re-evaluated.If the magnitude of the SOC difference is below a predeterminedthreshold, then cell balancing may be terminated. Note that somehysteresis may be incorporated into the thresholds for initiating andterminating cell balancing.

As discussed above, the SOC initialization-on-the fly technique may beapplied to ensure high-quality SOC estimations for each cell. When thepersistent excitation condition is met and the estimation convergencecondition is met, the SOC may be considered accurate. Cell balancing maybe initiated and terminated when high-quality SOC estimations areavailable for each cell.

FIG. 8 shows a flow chart of one possible implementation of a cellbalancing strategy. At system start 500, the controller may beginchecking for vehicle key-on 502. If key-on is not detected, thecontroller may continue to check the key-on condition 502. If key-on isdetected, the controller may start a timer, T_(cb) 504. The timer,T_(cb), may be used to ensure that the cell balancing is performedwithin a predetermined amount of time. The controller may then beginchecking for the SOC initialization-on-the-fly (SIOF) conditions 506.The SIOF conditions may be that persistent excitation and estimationconvergence conditions be satisfied.

If the SIOF conditions are met, the system may perform cell balancing508. At this point, SOC differences between the cells may be calculatedto ascertain whether or not cell balancing is required. If cellbalancing is necessary, then appropriate control actions may be taken(e.g., triggering appropriate switching devices). A check may then bemade as to ascertain if the cell balancing is complete 501. Completionmay require that the SOC difference magnitude be below a predeterminedmagnitude. If cell balancing is complete, the execution may end 518until started again. If cell balancing is not complete, the system maycontinue checking the SIOF conditions 506 and continue cell balancing508 while the SIOF conditions are met.

Should the SIOF conditions not be met, the system may check the statusof the timer T_(cb) 512 to ascertain if the timer has expired. Note thatthe timer may be implemented as a count up or count down timer.Expiration of the timer, T_(cb), indicates that a predetermined amountof time has elapsed. If the timer has not expired, the system maycontinue checking the SIOF conditions 506. If the timer has expired,then active battery excitation may be initiated 514. The active batteryexcitation request may ensure that the SIOF conditions are met. Afterinitiating active battery excitation, the SIOF conditions may be checked516. If the SIOF conditions are not met, the system may continuerequesting active battery excitation 514. If the SIOF conditions aremet, the system may continue cell balancing until completion.

The system may limit the number of cell balancing cycles within a singleignition cycle to be less than a predetermined number of cycles.Limiting the number of cycles during an ignition cycle helps to avoidexcessive cycling of the cell balancing logic in the event that the SOCestimation is inaccurate or that the cell balancing conditions are toonarrow.

Additionally, active excitation may be requested a predetermined amountof time after the cell balancing has been initiated if the SIOFconditions are not satisfied during cell balancing. This may help toensure that accurate SOC values are calculated during cell balancing. Inaddition, such a scheme may reduce the amount of time necessary for cellbalancing.

By activating the active excitation of the battery, improved parameterestimates may be obtained. Battery SOC may be derived from the parameterestimates. By ensuring that conditions are proper for estimation, thesystem may perform more effective cell balancing. In particular, thedetermination that SOC levels are equalized may be more accurate so thatcell balancing is more effective.

A battery control system may continuously calculate SOC and monitor thequality of the SOC during cell balancing. An advantage of the disclosedscheme is that a fixed cell balancing time is not necessary. Cellbalancing may continue until the SOC values are balanced with no needfor the balancing routine to run longer. Faster cell balancing times maybe achieved by requesting active excitation of the battery inputs duringcell balancing.

Scheduling Active Excitation Based on Quality of Parameter

Battery control signal accuracy (e.g., power capability and state ofcharge) using a model-based approach relies on parameter estimationaccuracy, particularly the r₁ resistance estimate. Power capabilityestimation error and state of charge estimation error may be expressedas a function of resistance r₁ estimation error as follows:

Power Capability Estimation Error∝I _(max) *Δr ₁  (35)

State of Charge Estimation Error∝I _(max) *Δr ₁  (36)

The resulting estimation errors are proportional to the maximum chargeor discharge current times the error in the resistance r₁ estimation.The resistance value may be expected to increase over the life of thebattery for a given battery temperature. A value used at the batterybeginning of life may not reflect the actual resistance value over timeas the value increases. Upper and lower limits of the battery parametersover time may be known such that, for a given battery age, a range ofexpected values may be defined. It is possible that if the batteryimpedance parameters are not learned over time that the currentresistance value may fall outside of the expected range. When the errorbecomes too large, it may be desirable to force the system to learn viaactive excitation.

The battery impedance parameters may be initialized using parameter databased on battery life. As described earlier, the battery parameters maychange over the life of the battery as a function of temperature andstate of charge. FIG. 6 depicts an example flow chart of how parameterlearning may be constructed. A preparation phase 300 may be initiated inwhich initial battery parameter values and tables are constructed. Aparameter table may be constructed that defines a profile for eachbattery impedance parameter based on state of charge and temperature.The parameter space may be divided into a grid of different intervals oftemperature and state of charge 302. The grid may be evenly spaced orunevenly spaced. The grid may be based on a partial derivative of theparameter with respect to temperature or state of charge. Thetemperature range (e.g., −40 C to 55 C for production battery) may bedenoted as T_(grid)=[1, . . . , N_(t)] and the state of charge grid maybe denoted SOC_(grid)=[1, . . . , N_(s)]. The grid may be initializedwith values from test data or expected values 304. For a beginning oflife battery, each grid may be associated with a time stamp denotedt_(stamp)(i,j) which may be initialized to zero. Each grid may have anassociated Quality Of Parameter Estimation, QOPE(i,j), value which maybe initialized to one. The grid may be retained in controller memorysuch that the data is available during subsequent ignition cycles.

The QOPE may be a value that indicates the past quality of theestimation. A value less than one may indicate that the learnedparameter set for the given indices (i,j) has larger variations. Ahigher value may indicate less variation over time and may represent amore reliable estimate of the parameter value.

Once the grid is initialized, the system may wait for the vehicle to keyon. At vehicle key on 306, the contactor may be turned on. Estimationmay not be performed if the contactor is not turned on. The contactormay be checked to verify that the contactor is on 308. If the contactoris not requested to turn on, then the system may continue checking thecontactor status 308. If the contactor is turned on, the system maybegin the parameter estimation process 310.

The system may then measure the temperature of the battery pack. Thecontroller may sample the temperature signal and store the result. Thebattery state of charge may also be evaluated. The state of charge maybe calculated using ampere-hour integration. Ampere-hour integration mayprovide a reasonable estimate at initialization as this technique doesnot rely on the equivalent circuit parameter learning. In addition, thebattery equivalent circuit parameters are less dependent on state ofcharge.

Knowing temperature and state of charge, the grid location for thecurrent operating point may be ascertained. By comparing the temperaturemeasurement to the elements of T_(grid), the controller may find theindex corresponding to the temperature measurement. Likewise, bycomparing the state of charge value to the elements of SOC_(grid), thecontroller may find the index corresponding to the current state ofcharge. The time stamp and quality of parameter estimation associatedwith the grid point (i,j) may then be read from t_(stamp)(i,j) andQOPE(i,j) respectively 312.

The battery may age via power capability fade (through increasing of theinternal resistance) and capacity loss (through loss of capabilities tohold ions in lithium-ion batteries). A calibration map (Timecal) may bedefined to describe the resistance increase over time. The calibrationmap may indicate a series of times at which the battery parameters areexpected to change. One method of obtaining the Timecal map may be touse a fixed interval that is dependent on the temperature and state ofcharge indices. Another method may be to use an adjustable timeinterval, that depends on temperature, state of charge, and the lengthof time the battery has been in operation. The adjustable time methodmay be derived from the observation that the battery aging (e.g.,internal resistance change) occurs at a different rate over time.Battery power and capacity fade may occur faster in the earlier stagesof battery life according to a root-square of time rule. The Timecal maybe denoted as Timecal(i,j) and may be a function of battery use time,temperature, and state of charge. The Timecal value may be updated overtime.

A projected quality of parameter may be calculated as

ProjQOP(i,j)=QOPE(i,j)*e ^(−α*(t-t) ^(stamp) ^((i,j)))  (37)

and a desired quality of parameter calibration may be expressed as

QOPcal(i,j)=e ^(−α(t-TimeCal(i,j)))  (38)

where t is the current time and a is a parameter for representinggradual decay of the parameter estimation quality over time.

An exponential decay function is shown above but other functions may beused so long as it is monotonically decreasing over time. QOPcal may becalculated directly from TimeCal and a so there is no need to storeQOPcal as a map. The learned parameter has an associated quality index.As time elapses, the quality index decays. When determining whether togenerate a new active excitation request, the projected quality index(ProjQOP) may be compared with a desired quality of parameter value(QOPcal) 314.

For example, consider the case in which the previously learned values,via active or passive excitation, for a given index (i,j) are the same.This indicates that the parameters at this index have not changed overtime. In this case, the learning appears to have yielded a proper value.Active learning should not be requested too often. Such a learningsequence may be given a high QOPE which provides a larger ProjQOP andless opportunity to request active learning.

As another example, consider the case in which the previously learnedvalues are significantly changed as measured by the standard deviationof the values. A low value of QOPE may be assigned to the learningsequence. A low QOPE provides a smaller ProjQOP which provides moreopportunity to request active learning.

A request to perform active learning 316 may be initiated whenProjQOP(i,j)<QOPcal(i,j). When this comparison is true, a flag may beset to request active excitation such that the parameters may be learnedduring active excitation of the traction battery. Hysteresis may beadded to prevent switching between states too quickly.

The projected QOPE value may start at a value defined by QOPE(i,j) anddecay over time from that value. Likewise, the desired quality ofparameter calibration may start at a value of one (when t=Timecal(i,j))and decay over time from that value. Over time, the Timecal value may bereset based on temperature, state of charge or battery use time. Whenthis occurs, the desired quality of parameter calibration may be resetto one making an active learning request more likely.

The system may operate so that a request to perform active excitation ofthe battery pack is based on the variability of previous parameterestimates and the time since the parameters were last estimated. As thevariability of the parameters increases, the time between activeexcitation requests may decrease. In addition, based on the observationthat parameters may change slower as the battery ages, the time betweenactive excitation requests may increase as the age of the batteryincreases.

The time and time stamp values may be based on an overall controllerglobal time. In other examples, the times may be based on a vehicle runtime, battery contactor on-time, or battery throughput. The time stampmay represent the time that the parameter was updated.

Once active excitation is requested, a check may be made to determine ifthe parameter learning was indeed successful 318. Parameter learning maybe checked using one or both of the persistent excitation condition andthe estimation convergence condition. If the parameter learning wassuccessful, parameter values may be retained for later use 320. Thecalculated QOPE and the associated time stamp may be written to memoryor EEPROM for the associated grid point. The learned parameters may bestored in a database as θ_(e)(i,j,k), where (i,j) are the grid indicesand k, an element of set [1,K], is a stack-like structure to storelearned parameters sequentially. If less than K data points have beenlearned, QOPE(i,j) may be set to one. If there are K entries in thedatabase and a new parameter is learned, the newly learned parameter maypush the oldest data out of the set.

When K data values have been learned, the standard deviation of the Kentries may be calculated. A map may be defined to calculate QOPE basedon the standard deviation: QOPE(i,j)=f(standard deviation of the Kvalues). If the standard deviation of the K entries is zero (i.e.,values all the same) then QOPE may be assigned a maximum value whichleads to a higher ProjQOP. If the standard deviation exceeds apredetermined threshold, the map may output a value less than oneleading to a lower ProjQOP. As the standard deviation increases, theinitial QOPE(i,j) may decrease.

Parameter estimates may be obtained using the model-based methodsdescribed above. The parameter estimates may be the result of passive oractive excitation. Additional criteria for the parameter estimates suchas persistent excitation or SIOF conditions may be checked. The schemedescribed attempts to decide when a new parameter estimate is needed fora given grid point based on the age and quality of the parameterestimate.

The above scheme may be used with other equivalent circuit models orparameterized electro-chemical models. The method of generating anactive excitation may result in more accurate parameter estimates. Theactive parameter learning request may be based on the past updatehistory of the parameters. Active learning may only be requested whenneeded based on the impact of the potential parameter error on thebattery control signal estimations. The learning time may be determinedbased on battery properties and learning history data quality ofestimation.

The above method may be implemented in one or more controllers as partof a powertrain control system or a vehicle power system. Activeexcitation may be requested based on variability of parameter estimatesand the age of the most recent estimate. As parameter variabilitydecreases, the time between active excitation requests may increase.

Performing Active Excitation

Prior art battery estimation may rely on voltage and currentmeasurements obtained during normal battery operation. Normal batteryoperation may attempt to optimize fuel efficiency or minimize systemlosses. Such normal operation may not be optimal for estimating thebattery parameters. The result may be that battery parameter estimatestake longer to converge or that the battery parameter estimates areinaccurate. To improve parameter estimation, it is possible to excitethe traction battery such that optimal conditions are present forparameter estimation.

A sufficient condition for accurate parameter estimation of theequivalent circuit model parameters is that the input signal contains atleast one distinct frequency component for each two unknown parameters.These frequency components must have high signal-to-noise (SNR) in theinput signal. The battery power demand profile must contain more thantwo distinct frequency components to achieve a quality estimation usingthe simplest model.

During vehicle operation, the persistent excitation conditions may notbe satisfied or may only be weakly satisfied. One method to analyze thesufficiency of the battery power demand may be to analyze the frequencycontent of the battery power demand signal. In order to properlyestimate the battery parameters, it may be desirable that the batterypower demand vary over time. For example, during extended cruise controloperation at a steady speed, the conditions may not be satisfied. Duringsteady state speeds, the battery power demand may be at a nearly steadyvalue. This constant value may not excite enough frequencies to allowfor accurate estimation. The frequency component magnitudes may need tobe above any noise signals to allow for identification of theparameters. During vehicle operations where the battery power demand isvaried, the conditions are more likely to be satisfied. That is, themagnitude of the frequency components may be large enough to allowidentification of the parameters. When the conditions are satisfied, thebattery parameter estimation may be more accurate.

Inaccurate parameter estimation or infrequent update of the parametersmay lead to inaccurate battery control values, such as state of chargeand battery power capability, being calculated. For example, batterypower capability may be incorrect which may impact battery durabilityand lifetime. Battery state of charge may be inaccurate which may impactvehicle system control and the energy management strategy. Fuel economyor energy efficiency during vehicle operation may be degraded.

An example of when persistent excitation criteria may not be satisfiedis during generally constant battery power demands. This may occurduring drive cycles in which a constant or steady speed is maintained.During a generally constant battery power demand, there may be little orno variation in the battery power that is supplied by the battery. Whenanalyzed in the frequency domain, frequency component amplitudes for agiven range of frequencies may be relatively low. In fact, if the powerdemand is constant there may only be a zero frequency amplitude.

As another example, consider a sinusoidal battery power demand thatvaries at a constant frequency at some magnitude. In this case, thefrequency component amplitude at the constant frequency may be greaterthan the amplitude found at other frequencies. When plotting amplitudeversus frequency a spike at the constant frequency may be observed. Asadditional frequency components are added to the battery power demandthe amplitude values at the different frequencies will increase.

As discussed above, the control system may passively perform parameterestimation by waiting for the conditions to be satisfied. Alternatively,a request to actively control the battery power demand to satisfy theconditions may be initiated. The control strategy for actively modifyingthe battery power demand may require several functions. A battery systemstate monitoring function may determine when to generate an activesystem excitation request. A battery system excitation input signalpattern recognition function may determine the battery power inputformat and frequency components. A battery system excitation outputfunction may issue commands to realize the desired battery system input.

The format of the battery power demand signal may need to be determined.In general, a battery power demand signal may be selected that forms acertain predefined pattern for a short time period with a number ofdistinct and dominating frequency components n>N/2, where N is the totalnumber of system parameters to be identified. This condition may beconsidered to be the frequency domain equivalent of the persistentexcitation condition described previously. In practice, the shape of theexcitation input pattern must be specified such that the resultingbattery power demand has significant magnitude, but constrained with thebattery power limits. Without a loss of generality, a candidate signal,P may be generated as:

P _(batt) _(—) _(atv)=Σ_(i=1) ^(n) A _(i) sin(ω_(i)+φ_(i))  (39)

where ω and φ are the angular frequency and phase of the i-th frequencycomponent and A_(i) is the magnitude of the i-th component. In addition,the active battery power pattern should comply with battery SOCconservation requirements.

During periods of generally constant battery power demand, when viewedin the frequency domain, a range of frequency component amplitudes ofbattery power demand may be less than a predefined magnitude. Activeexcitation causes a predetermined number of the frequency componentamplitudes to exceed the predefined magnitude by modifying the batterypower demand. The specific range and predefined magnitude may bedependent upon the particular battery impedance parameters.

In an electrified vehicle, the battery power demand, P_(batt), tosatisfy a given driver power demand, P_(whl), may be determined asfollows:

P _(eng) +P _(batt) −P _(loss) −P _(acc) =P _(whl)  (40)

P _(drv) =P _(whl) −P _(brk) −P _(load)  (41)

where P_(eng) is engine power, P_(batt) is battery power, P_(loss) isthe powertrain power loss, P_(acc) is the accessory power load, P_(whl)is the propulsion wheel power, P_(drv) is the driver demand, P_(brk) isthe braking wheel power, and P_(load) is the external power loads. Underdriving conditions, P_(whl) must satisfy the driver demand.

One possible method of altering the battery power demand is to adjustthe power demand allocation in the vehicle system control domain. Theoverall power distribution may be distributed between the engine and thebattery by controlling a power distribution between an engine poweroutput and an electric machine power output. The desired battery powerdemand may be generated at a given wheel power demand level as:

P _(batt) =P _(whl) +P _(loss) +P _(acc) −P _(eng) =P _(batt) _(—)_(atv)  (42)

When setting the battery power to the candidate signal, the engine powermay be adjusted to compensate as follows:

P _(eng) =−P _(batt) _(—) _(atv) +P _(whl) +P _(loss) +P _(acc)  (43)

FIG. 7 shows a power flow diagram for the system depicting the aboveequations.

When considering normal power distribution between the battery andengine, the switches (418, 420, 422, 424) may be considered open. Thesystem may calculate an engine power (P_(eng)) 400 and a battery power(P_(batt)) 402 to meet specified performance objectives such as systemefficiency while meeting the overall driver demand (P_(drv)) 414. Thetotal power supplied by the engine and battery (P_(tot)) 428 is the sumof the engine and battery powers. Note that battery electrical power maybe converted to mechanical power by an electric machine. Power isrequired to account for losses (P_(loss)) 404 and accessory powerconsumption (P_(acc)) 406. A power at the wheel is determined (P_(whl))410 based on the power supplied by the battery and engine minus theselosses and accessory loads. The power output from the drivetrain(P_(drv)) 414 is the power delivered to the wheel 410 minus any brakingpower (P_(brk)) 408 and minus any vehicle load (P_(load)) 412.

P_(whl) 410 may be a total power from the engine and electric machinesdelivered to the wheels of the vehicle. The wheel power reflects thetorque applied at the wheel which is a function of the engine torque andthe electric machine torque. The losses, P_(loss) 404, may be powertrainlosses that include transmission efficiencies and rotating losses. Theselosses may also include electric machine and power electronicsefficiencies and losses.

During active excitation, the battery power demand may be set to apattern that sufficiently excites the system so that parameterestimation accuracy may be improved. The engine power should not bepermitted to violate any engine power limits and abrupt changes inengine speed or torque may be limited. The total power from the engineand battery may remain the same, the distribution of the power providedbetween the two may be altered to provide sufficient excitation forbattery parameter estimation. When more battery power is provided, lessengine power is needed.

An adjustment to battery power is depicted in FIG. 7 as an activeexcitation power addition ΔP_(batt) _(—) _(atv) 416. The additionalbattery power may be a positive or negative quantity that makes P_(batt)equal to P_(batt) _(—) _(atv) as discussed above. When using the engineto offset the battery power addition, any increase in battery powersupplied may lead to a decrease in engine power supplied. Any decreasein battery power supplied may lead to an increase in engine powersupplied. In this mode of active excitation, switches S1 (418) and S2(420) may be closed. The additional power ΔP_(batt) _(—) _(atv) 416 maybe added to P_(batt) (402) to give an adjusted battery power P′_(batt)430. The additional power ΔP_(batt) _(—) _(atv) 416 may be subtractedfrom the engine power P_(eng) 400 to give an adjusted engine powerP′_(eng) 426. In this mode, the total power output P_(tot) 428 may bethe same as before (that is, without the addition of ΔP_(batt) _(—)_(atv) 416). This mode merely adjusts the relative power contributionbetween the engine and the battery.

Another possible method of altering the battery power demand may be toalter the accessory power, P_(acc). This may be achieved by controllingpower consumed by an electrical load. The above equations apply exceptthat engine power is not changed, but an accessory load power may bechanged. The resulting equation is:

P _(acc) =P _(eng) +P _(batt) _(—) _(atv) −P _(whl) −P _(loss)  (44)

In this case, as more battery power is provided, the accessory load isoperated to use the additional battery power.

This method may be analyzed from FIG. 7 by closing switch S1 (418) andswitch S3 (422). Battery power may be adjusted by ΔP_(batt) _(—) _(atv)416 to yield an adjusted battery power P′_(batt) 430. The accessorypower P_(acc) 406 may be incremented by ΔP_(batt) _(—) _(atv) 416 aswell to yield P′_(acc) 432. In this mode, the additional power is drawnfrom the battery to supply an increased demand from the accessory loads.Modifying the accessory load may require close coordination withassociated controllers to increase a power demand for accessory load.

Another possible method of altering the battery power demand may bethrough wheel torque cancellation. Torque cancellation applies an activebrake torque to boost the propulsion wheel torque above the normal drivepower demand plus load torque level. The effect may be achieved bycontrolling an electric machine power output and operating a wheel braketo offset the changes in the electric machine power output. As P_(brk)is increased, P_(whl) may be increased to compensate. The increase inP_(whl) may be accomplished with additional battery power, P_(batt). Inthis manner, P_(brk) and P_(batt) may be altered using P_(batt) _(—)_(atv) to achieve the desired battery power demand excitation.

This method may be analyzed from FIG. 7 by closing switch S1 418 andswitch S4 424. Battery power may be adjusted by ΔP_(batt) _(—) _(atv)416 to yield an adjusted battery power P′_(batt) 430. The brake powerP_(brk) 408 may be incremented by ΔP_(batt) _(—) _(atv) 416 as well toyield P′_(brk) 434. In this mode, the power absorbed by the brakingsystem may be supplied by the battery.

Wheel torque cancellation may require close coordination with thebraking system to apply a braking force to the wheels. Additionally,coordination with the battery controller and power electronics modulemay be necessary. The power electronics module may be required to changethe mechanical power output of an electric machine to supply the extrapower absorbed by the brakes.

In all of the cases described, the power delivered P_(drv) 414 remainsthe same. The vehicle and powertrain delivers and absorbs power in sucha manner as to be transparent to the vehicle operator. Any additionalpower added into the drivetrain may be absorbed by other components suchthat the output power remains constant. Since the power at the wheel forpropulsion remains the same in each case, the traction batteryexcitation does not affect the vehicle acceleration. The systemdescribed creates a condition for improved battery excitation withoutaffecting acceleration of the vehicle.

Note that in FIG. 7, the switches are merely illustrative of how thesystem is intended to operate. In practice, the logic may be implementedin the controller and no physical switches are necessary.

There are several situations in which active battery power excitationmay be useful. One situation may be during cold start conditions. Thebattery system may be equipped with a temperature control system tomaintain the battery operation within a certain temperature range. Undercold start conditions it may be desired to accurately estimate thebattery parameters. To guarantee that the parameters may be accuratelylearned, the active excitation scheme may be initiated.

The battery system parameter values are also dependent on the batterySOC. At certain SOC levels, the battery parameters may not be learnedunless the system estimation conditions are satisfied. They may beobserved in PHEV and BEV as the battery depletes from a high SOC to alow SOC during vehicle operation. At certain SOC levels, the activeexcitation may be initiated to allow accurate parameter estimation.Accurate knowledge of the battery parameters is important for batterysystem protection and durability. In addition, accurate knowledge of theparameters helps to achieve consistent performance and fuel economy.

The active excitation system described may find most usage duringperiods of generally constant battery power demand. During a period ofgenerally constant battery power demand, the frequency componentamplitudes over a given range may be less than some threshold. This mayindicate that the persistent excitation criteria may not be satisfied.When a condition is identified in which active excitation is needed, thebattery power demand may be adjusted in order to cause the desirednumber of frequency component amplitudes to exceed a threshold value.The range of frequencies and the magnitude of the frequency componentamplitudes may be based on expected battery impedance parameters. Theactive excitation system may then operate various vehicle systems toachieve the desired battery power demand without affecting accelerationof the vehicle.

The active excitation may be implemented as part of a powertrain controlsystem for a vehicle. The system described may require coordinationbetween multiple systems or controllers. An electrical load may need tobe controlled and may have an associated controller. The electricmachine power may need to be controlled and may have an associatedcontroller. The engine may require operational changes as well. Thecontrollers may communicate via a network to coordinate operations. Acoordinating controller that implements the algorithm may be part of apowertrain control system and may communicate with the other controllersto achieve the desired operation.

The processes, methods, or algorithms disclosed herein can bedeliverable to/implemented by a processing device, controller, orcomputer, which can include any existing programmable electronic controlunit or dedicated electronic control unit. Similarly, the processes,methods, or algorithms can be stored as data and instructions executableby a controller or computer in many forms including, but not limited to,information permanently stored on non-writable storage media such as ROMdevices and information alterably stored on writeable storage media suchas floppy disks, magnetic tapes, CDs, RAM devices, and other magneticand optical media. The processes, methods, or algorithms can also beimplemented in a software executable object. Alternatively, theprocesses, methods, or algorithms can be embodied in whole or in partusing suitable hardware components, such as Application SpecificIntegrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs),state machines, controllers or other hardware components or devices, ora combination of hardware, software and firmware components.

While exemplary embodiments are described above, it is not intended thatthese embodiments describe all possible forms encompassed by the claims.The words used in the specification are words of description rather thanlimitation, and it is understood that various changes can be madewithout departing from the spirit and scope of the disclosure. Aspreviously described, the features of various embodiments can becombined to form further embodiments of the invention that may not beexplicitly described or illustrated. While various embodiments couldhave been described as providing advantages or being preferred overother embodiments or prior art implementations with respect to one ormore desired characteristics, those of ordinary skill in the artrecognize that one or more features or characteristics can becompromised to achieve desired overall system attributes, which dependon the specific application and implementation. These attributes mayinclude, but are not limited to cost, strength, durability, life cyclecost, marketability, appearance, packaging, size, serviceability,weight, manufacturability, ease of assembly, etc. As such, embodimentsdescribed as less desirable than other embodiments or prior artimplementations with respect to one or more characteristics are notoutside the scope of the disclosure and can be desirable for particularapplications.

What is claimed is:
 1. A battery control system for a vehiclecomprising: a traction battery including a plurality of cells; and atleast one controller programmed to generate model parameter estimatesfor the traction battery and, in response to a persistent excitationcondition and an estimation convergence condition being satisfied,operate the traction battery according to a state of charge derived fromthe model parameter estimates.
 2. The battery control system of claim 1wherein the persistent excitation condition is satisfied when${\alpha_{0}I} \geq {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{20mu} {i(\tau)}\mspace{20mu} \frac{{i(\tau)}}{\tau}} \right\rbrack^{T}*{\quad{{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{20mu} {i(\tau)}\mspace{20mu} \frac{{i(\tau)}}{\tau}} \right\rbrack {\tau}} \geq {\alpha_{1}I}}}}}}$is satisfied, where T_(pe) is an integration interval, V_(t) is aterminal voltage, V_(oc) is an open circuit voltage, i is a current, andα₀ and α₁ are predetermined values.
 3. The battery control system ofclaim 1 wherein the estimation convergence condition is satisfied whenan error magnitude between at least one of the model parameter estimatesand a corresponding measured model parameter value is less than apredetermined threshold for a predetermined period.
 4. The batterycontrol system of claim 1 wherein the at least one controller is furtherprogrammed to, in response to at least one of the persistent excitationcondition and the estimation convergence condition not being satisfied,cause a predetermined number of frequency component amplitudes ofbattery power demand to exceed a predetermined magnitude withoutaffecting acceleration of the vehicle.
 5. The battery control system ofclaim 1 wherein the at least one controller is further programmed tooperate the traction battery according to a battery capacity derivedfrom a first state of charge and a second state of charge, wherein thesecond state of charge is evaluated after detecting at least apredetermined amount of current throughput from when the first state ofcharge was evaluated.
 6. The battery control system of claim 5 whereinthe first state of charge and the second state of charge are evaluatedwithin a common ignition cycle.
 7. The battery control system of claim 5wherein the first state of charge and the second state of charge areevaluated when a battery temperature is above a predeterminedtemperature.
 8. The battery control system of claim 5 wherein the atleast one controller is further programmed to schedule the first stateof charge and the second state of charge to be evaluated within apredetermined time window.
 9. The battery control system of claim 8wherein the at least one controller is further programmed to schedulethe predetermined time window such that a time between successivepredetermined time windows increases as an age of the traction batteryincreases.
 10. The battery control system of claim 8 wherein the atleast one controller is further programmed to, in response to at leastone of the persistent excitation condition and the estimationconvergence condition not being satisfied within the predetermined timewindow, cause a predetermined number of frequency component amplitudesof battery power demand to exceed a predetermined magnitude withoutaffecting acceleration of the vehicle.
 11. A vehicle comprising: atraction battery including a plurality of cells; and at least onecontroller programmed to generate model parameter estimates for thetraction battery and, in response to a persistent excitation conditionnot being satisfied, cause a predetermined number of frequency componentamplitudes of battery power demand to exceed a predetermined magnitudewithout affecting acceleration of the vehicle.
 12. The vehicle of claim11 wherein the persistent excitation condition is not satisfied when${\alpha_{0}I} \geq {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{20mu} {i(\tau)}\mspace{20mu} \frac{{i(\tau)}}{\tau}} \right\rbrack^{T}*{\quad{{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{20mu} {i(\tau)}\mspace{20mu} \frac{{i(\tau)}}{\tau}} \right\rbrack {\tau}} \geq {\alpha_{1}I}}}}}}$is not satisfied, where T_(pe) is an integration interval, V_(t) is aterminal voltage, V_(oc) is an open circuit voltage, i is a current, andα₀ and α₁ are predetermined values.
 13. The vehicle of claim 11 whereinthe at least one controller is further programmed to, in response to anestimation convergence condition not being satisfied, cause apredetermined number of frequency component amplitudes of battery powerdemand to exceed a predetermined magnitude without affectingacceleration of the vehicle.
 14. The vehicle of claim 13 wherein theestimation convergence condition is not satisfied when an errormagnitude between at least one of the model parameter estimates and acorresponding measured model parameter value is greater than apredetermined threshold.
 15. A method of operating a traction batterycomprising: scheduling a time window in which to learn a batterycapacity; in response to a persistent excitation condition and anestimation convergence condition being satisfied during the window,learning a first state of charge value and, after the batteryexperiences a predetermined amount of current throughput, learning asecond state of charge value; and operating the traction batteryaccording to the battery capacity derived from the values.
 16. Themethod of claim 15 wherein the persistent excitation condition issatisfied when${\alpha_{0}I} \geq {\frac{1}{T_{pe}}*{\int_{t_{0}}^{t_{0} + T_{pe}}{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{20mu} {i(\tau)}\mspace{20mu} \frac{{i(\tau)}}{\tau}} \right\rbrack^{T}*{\quad{{\left\lbrack {\frac{\left( {{V_{t}(\tau)} - {V_{oc}(\tau)}} \right)}{\tau}\mspace{20mu} {i(\tau)}\mspace{20mu} \frac{{i(\tau)}}{\tau}} \right\rbrack {\tau}} \geq {\alpha_{1}I}}}}}}$is satisfied, where T_(pe) is an integration interval, V_(t) is aterminal voltage, V_(oc) is an open circuit voltage, i is a current, andα₀ and α₁ are predetermined values.
 17. The method of claim 15 whereinthe estimation convergence condition is satisfied when an errormagnitude between an estimated model parameter and a correspondingmeasured model parameter value is less than a predetermined thresholdfor a predetermined period.
 18. The method of claim 15 furthercomprising causing, in response to at least one of the persistentexcitation condition and the estimation convergence condition not beingsatisfied within the time window, a predetermined number of frequencycomponent amplitudes of battery power demand to exceed a predeterminedmagnitude without affecting vehicle acceleration.
 19. The method ofclaim 15 wherein the first and second state of charge values are learnedwhen a battery temperature is above a predetermined temperature.
 20. Themethod of claim 15 wherein the time window is scheduled such that thetime between successive time windows increases as an age of the tractionbattery increases.